Question

Resolva as equações:

a)
${x}^{4} - 16 {x}^{2} = 0$
b)
${x}^{4} - 3 {x}^{2} - 4 = 0$
c)
${x}^{4} - 81 = 0$
d)
${x}^{4} - {x}^{2} = 0$

Answer 1

a. x^4 - 16x^2 = 0
(x^2)^2 - 16x^2 = 0
y = x^2
y^2 - 16y = 0
y^2 = 16y
y^2÷y^1 = 16
y = 16 | x^2 = 16 | x = √16 = +-4

b. x^4 - 3x^2 - 4 = 0
(x^2)^2 - 3x^2 - 4 = 0
y = x^2
y^2 - 3y - 4 = 0
(3+-√9-4×(-4))÷2
(3+-√9+16)÷2
(3+5)÷2 = 8÷2 = 4
(3-5)÷2 = -2÷2 = -1
x^2 = 4 | x = √4 = 2
x^2 = -1 | x = √-1

c. x^4 - 81 = 0
(x^2)^2 - 81 = 0
y = x^2
y^2 - 81 = 0
y^2 = 81
y = √81 = 9
x^2 = 9 | x = √9 = 3

d. x^4 - x^2 = 0
(x^2)^2 - x^2 = 0
y^2 - y = 0
y^2 = y = 1 ou 0
x^2 = 1 | x = √1 = 1
x^2 = 0 | x = √0 = 0